I will review some recent work on spontaneous partial supersymmetry breaking in extended supersymmetry. I will first describe the no-go theorems which forbid N=2 to N=1 spontaneous supersymmetry breaking in global and local supersymmetry, before showing how they are circumvented. I will then discuss some new techniques involving the embedding tensor formalism which allow us to study this problem systemically and find the low-energy effective theory in the N=1 vacuum. This leads to interesting insights into spontaneous partial supersymmetry breaking in supergravity and string theory, as well as new results in quaternionic geometry.

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